Unit Analysis Problem Solving: 

Chemistry word problems sometimes may be difficult. There are several methods for solving chemical word problems. A powerful technique for solving problems is called unit analysis method, sometimes referred to as dimensional analysis method, or factor label method of problem solving. Unit analysis cannot solve every chemistry word problem, but it is very effective for the problems we encounter in beginning and college chemistry.

Corwin's Text: Chapter 2 Section 2.9

three steps to solve word problems

How do you approach Word Problems?

Image of One Liter Box

tudents fall into three categories, maybe four, when trying to solve simple word problems. Some are number jugglers. Some are formula freaks. Others understand how to word juggle, while a fourth just becomes frustrated and will anything to avoid a word problem. The fourth just freezes at a word problem and just walks away. Which best fits you?

Solving problems by unit analysis is a simple three step process:

Step 1. Read the problem and determine the unit required in the answer.

Step 2. Analyze the problem and determine the given value related to the answer.

Step 3. Apply unit factors to convert the unit of the given to the unit in the answer.

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Sample Problems

Problem 1
If the sun is 93,000,000 miles from the Earth, how many kilometers is the distance?
(Given: One mile equals 1.61 kilometers.)

Problem 2
If the sun is 93,000,000 miles from the Earth, how many minutes does it take for sunlight to reach the Earth? (Given: The velocity of light is 186,000 miles per second.)

Problem 3
Find the mass in grains of a 325 milligram aspirin tablet.
(Given: 1.00 g = 15.4 grains)

Problem 4
Insurance statistics state that a person loses 8 minutes of average life for each cigarette smoked. If there are 20 cigarettes in a pack and the average cost of cigarette is $5.00 per pack over the next 25 years, how many years of average life would a person lose for smoking 1.5 packs a day for 25 years?

Problem 5
What is the density of water in lb/ft3, if the density of water at 25oC is 1.00 g/ml?
[Hint: There are 2.54 cm = 1 in (or 16.48 cm3 = 1 in3); 454 g = 1 lb ]

Problem 6
Calculate the velocity of a car traveling car traveling 65 miles/hr in ft/sec.

Problem 7
How many milligrams does a 0.750 carat diamond weigh?
(Hint: 1 carat = 0.200 g)

Problem 8
Diamond has a density of 3.513 g/cm3. The mass of a diamond is often measured in carats, 1 carat equaling 0.200 g. What is the volume of a 1.50 carat diamond?

Problem 9
Liquor used to be sold in fifths. A fifth is one fifth of a gallon. A gallon is 128 fluid ounces. Today liquor is sold in bottle sizes of 750 ml to equate to the old fifth. If there are 946 ml in a quart, calculate the number of milliliters in a fifth. How many milliliters difference is there in the bottling?

The True Story
On July 23, 1983, Air Canada Flight 143 was flying at an altitude of 26,000 ft from Montreal to Edmonton. Warning buzzers sounded in the cockpit of the Boeing 767. One of the world's larger planes was now a glider-the plane had ran out of fuel! Like all Boeing 767s, the plane had a sophisticated fuel gauge, but it was not working properly. However, the plane was still allowed to fly, because there is an alternate method for determining fuel. The Mechanics have a dip stick, calibrated in centimeters, and translated into volume in liters. The Mechanics calculated the three tanks had a total of 7682L of fuel. Pilots always calculate fuel quantities in mass, because they need to know the total mass of the plane before takeoff. Air Canada pilots had always calculated the mass in pounds, but the new 767s fuel consumption was given in kilograms. This involved using the fuel's density to convert 7682 L to a mass in kilograms, so that the pilot could calculate the mass of fuel that had to be added. The First Officer of the plane asked the Mechanic for the conversion factor to calculate volume-to-mass conversion, and the Mechanic replied "1.77". Using that number, the officer and the Mechanic calculated that 4917 L of fuel should be added. The required amount for the trip was 22,300 kg. The mechanic never gave the First Officer the conversion units which was for pounds per liter, not kg/liter as the First Officer assumed. The rest of the story is that the Pilot could not make it to the nearest airport, Winnipeg, but to a little town Gimli which had a former Royal Canadian Air Force runway converted to a race track. For 30 minutes the plane glided to Gimil and managed to land.

Now The Problem 10
The Gimli Glider was a Boeing 767 that ran out of fuel. Read the story above, then verify that the ground crew should have added 20,163 L of fuel instead 4916. The crucial piece of information is the density of the fuel. The crew used 1.77, but did not recognize the units were pounds per liter. To solve the problem you need first to find the density in units of kilograms per liter (Hint: 1 lb = 453.6 grams).

Problem Reworded

1. On July 23, 1983 Air Canada Flight 143, flying at 26,000 feet from Montreal to Edmonton, ran out of fuel because the first officer ask the mechanic for the conversion factor of mass to volume at Montreal. The mechanic gave the first officer the answer 1.77 with no units. The plane had 7682 L of fuel at Montreal. The pilot knew he needed 22,300 kg of fuel to make the trip. The mechanic's answer of 1.77 was pounds per liter not kilograms per liter caused the error such that only 4917 L of fuel was added. If there are 2.205 pounds in a kilogram, how many liters of fuel were needed for the trip? How many liters minimum of fuel should have been added at Montreal before takeoff?

Problem 11

Before 1982 the US Mint cast penny coins from an alloy of copper and zinc. A 1980 Penny weighs 3.051 g and contains 2.898 g of pure copper. In 1982 the US Mint stopped making copper pennies, because the price of copper was worth more than the penny. The post 1982 penny contains only a layer of copper over zinc. A 1990 penny weighs 2.554 g and contains 2.490 g of zinc. If the mint melted down one pound of 1980 pennies, how many 1990 pennies can be made from the total copper from the 1980 pennies?

Problems 12

An Olympic size swimming pool is 50.0 m long and 25.0 m wide. How many gallons of water ( d = 1.0g/mL )are needed to fill the pool to an average depth of 5.5 feet.

Problem 13

A furniture factory needs 29.5 ft2 of fabric to upholster one chair. A Europen supplier sends the fabric in bolts of exactly 200 m2. What is the maximum number of chirs that can be upholstered by three bolts of fabric. Hint: 1 m - 3.281 ft)?

Problem 14

My throw away car gets 23.4 mi/gal and hold 70.1 L of gasoline. How far can I drive on a tankful of gas?

If gas cost $2.20/gal; how much does a tankful of gas cost?

If the average speed on a trip is 92.2 km/hr, How many hours may I drive the car on the trip before I run out of gas?

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